Question

solve x2 - 8x = 3 by completing the square. which is the solution set of the equation ?

Answer 1

x²-8x=3
x²-8x+16=3+16=19
(x-4)²=19
x-4=±√19
x=4±√19
x=8.3589 approx or x=-0.3589 approx {4-√19,4+√19} or {-0.3589,8.3589}

Answer 2

we know that

$(x-a)^{2}=x^{2}-2ax+a^{2}$

in this problem we have

$x^{2} - 8x = 3$

so

equate

$-8x=-2ax\\2a=8\\a=4$

substitute

$(x-4)^{2}=x^{2}-8x+16$

therefore

$x^{2} - 8x = 3$

$x^{2} - 8x+16 = 3+16$

$x^{2} - 8x+16 = 19$

rewrite as perfect square

$(x-4)^{2} = 19$

$(x-4) =(+/-)\sqrt{19}\\x=(+/-) \sqrt{19}+4$

therefore

the answer is

the solution set is

$x1= 4+\sqrt{19}\\x2=4- \sqrt{19}$